Here's a series of charts I compiled, comparing the various OD&D saving throw categories (click image to expand).
These graphs chart the saves at every individual level in OD&D, and also insert linear regression lines ("trend lines", or "lines of best fit"). They incorporate all the data from levels 1 to 15. I think this highlights certain patterns which are not obvious in the tables (granted the differing ways the class levels are grouped), and may even disabuse a few common misconceptions.
One of the first things to be seen is how the class save values are grouped (Fighters in blocks of 3 levels, Clerics 4, Wizards 5). Some of us would like to smooth this out from the table values, permitting a small improvement every level or so (as suggested for fighter to-hits in the AD&D DMG, or the Lakofka/Gygax Dragon article noted here) -- so the trend lines are useful for that.
A second thing is that wizards (magic-users) tend to have a shallower trend line, improving more slowly than the other classes. This is partly because there is another higher-level category for wizards (levels 16+) which is not shown here. Ultimately wizards end up with saves as good as (or better than) the other classes, but that doesn't occur until the very high levels off these charts.
Now for some more specifics. Fighters and Clerics are extremely close in almost all their values and trends, to the extent where I'll simply regard them as effectively the same. Similarly, in the last chart, saves vs. Spells are practically identical for all the classes at all levels; at most a difference of +/-1 in the trend at any level. Saves vs. Stone are somewhat more mixed; the trend lines actually cross (Fighters start out the worst, then become the best), but are so closely packed that we may as well treat them as basically the same, as well.
Finally, some differences. Wizards (and hence Thieves, as per Greyhawk) are clearly, consistently deficient in their Death and Wands saves from levels 1-15. Also, while starting out fairly close, Fighters have a particularly steep (beneficial) trend line in Breath saving throws. Therefore on average, wizards are at -3 when compared to Fighters across all these categories (Wands, Death, and Breath; technically average -2.67, -2.67, -3.47 respectively). Even clerics are at a -2 average penalty when compared to fighters in the solitary category of Breath saves (-2.33, to be exact).
It's interesting that if you take Fighters as the basic character class (including all monsters), the baseline saves differ, on average, by precisely 1 point per category. That is, starting with the last category of Spells, Breath is at +1, Stone at +2, Wands +3, and Death +4 (again speaking in terms of the trend line intercept parameter; you can also see it immediately in the top row of the OD&D table itself).
The trend lines move downward with an average slope of -0.6 over all saves and classes (with a range of from -0.45 for the shallow wizard lines to -0.8 for the quickly advancing fighters vs. breath saves). If we think about smoothing out the curves with a simple formula (instead of using the tables directly), we might think about giving a bonus of half-the-level as a pretty good estimate. Of course, in my OED rules editorial, I felt even that was too complicated, and simply rounded it off to d20+level (beat 20+), plus the various modifiers noted above.